Question

If the areas of two similar triangles are equal, they are also congruent.

• A. True
• B. False

Answer 1

The correct option is A

True

$\frac{A_1}{A_2}=\frac{s_1^2}{s{{}^{\prime }}_1^2}=\frac{s_2^2}{s{{}^{\prime }}_2^2}=\frac{s_3^2}{s{{}^{\prime }}_3^2}But{A}_1=A_2\frac{s_1^2}{s{{}^{\prime }}_1^2}=\frac{s_2^2}{s{{}^{\prime }}_2^2}=\frac{s_3^2}{s{{}^{\prime }}_3^2}=1\Rightarrow s_1=s{{}^{\prime }}_1,s_2=s{{}^{\prime }}_{2}and{s}_3=s{{}^{\prime }}_3.\therefore {△}^{\prime }isarecongruent\left(BySSScongruence\right)$